You can't go by how many chances there are absolutely, but by the ratio of possible wins to losses. So you have to take into account the total amount. 13,999,993/14,000,000 is close to 1,999,999/2,000,000, even though there is a difference of 12,000,000. Your approach of just look at the possibility of wins is inappropriate. For example, if you have a 50% chance of winning in the 14,000,000, or 7,000,000 this is about 5,000,000 more chances of losing than 1,999,999 out of 2,000,000, but its clearly the better option. An even easier example would be 1/5 chance versus a 5/10 chance. There's 4 ways to lose in the first one, and 5 ways to lose in the 2nd, but 5/10 = 1/2 is a much higher chance of winning than 1/5.